Mathematics BSc
Course description
2013.

Number theory 1
Hours
lect+pc
Credits
lect+pc
Assessment Specialization Course code
lect/pc
Semester Status
2 + 2 2 + 3 exam +
term grade
all mm1c1se1
mm1c2se1
1 compulsory
Strong Weak Prerequisites
Lecture
Weak:
practice class
Prerequisites
High school mathematics.
Course objectives
The course presents an introduction to number theory.
Literature
  • G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers. Online edition.
Syllabus
  • Divisibility, greatest common divisor, the Euclidean algorithm, prime numbers, the fundamental theorem of arithmetic.
  • Special arithmetic functions, additive and multiplicative arithmetic functions. Divisor sum of multiplicative functions. The Möbius function. Perfect numbers.
  • Congruences. The Euler-Fermat theorem. Linear congruences and diophantine equations. Linear congruence systems. Applications in computational number theory.
  • Congruences of higher degree. Reduction to prime power, resp. prime moduli. Number of solutions, the reduction of degree in case of prime moduli. Wilson's theorem. Binomial congruences, order, primitive roots, index. Quadratic residues, the Legendre symbol, Euler's lemma.
  • There are infinitely many primes, the estimate of π(x).